On the computation of nonnegative quadrature weights on the sphere

DOI10.1016/j.acha.2008.12.003zbMath1166.65322OpenAlexW1983995930MaRDI QIDQ1026469

Daniel Potts, Stefan Kunis, Manuel Gräf

Publication date: 25 June 2009

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2008.12.003

zbMATH Keywords

algorithmsnumerical examplesquadraturecubature formulatwo-spherecomputation of nonnegative quadrature weightsnonequispaced fast spherical Fourier transform

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (16)

Zooming from global to local: a multiscale RBF approach ⋮ Sampling Sets and Quadrature Formulae on the Rotation Group ⋮ \(L_2\) error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data ⋮ Analytical study of cubature formulas on a sphere in computer algebra systems ⋮ Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere ⋮ Uniform approximation on the sphere by least squares polynomials ⋮ A continuous energy-based immersed boundary method for elastic shells ⋮ Hyperinterpolation for Spectral Wave Propagation Models in Three Dimensions ⋮ On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms ⋮ Kernel based quadrature on spheres and other homogeneous spaces ⋮ Local numerical integration on the sphere ⋮ On spherical harmonics based numerical quadrature over the surface of a sphere ⋮ Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions ⋮ Regularized collocation for spherical harmonics gravitational field modeling ⋮ The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems ⋮ Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere

Uses Software

• BCLS
• NFFT
• Healpix

Cites Work

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• Distributing many points on a sphere
• Multivariate polynomial approximation
• Fast spherical Fourier algorithms.
• Polynomial interpolation and hyperinterpolation over general regions
• Efficient reconstruction of functions on the sphere from scattered data
• Linear programming. Foundations and extensions.
• Lagerung von Punkten auf der Kugel
• Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
• Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere
• Polynomial approximation on the sphere using scattered data
• Fast evaluation of quadrature formulae on the sphere

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